Part A:
The experimental probability of rolling a 6 can be calculated using the formula:
\[ \text{Experimental Probability} = \frac{\text{Number of times 6 is rolled}}{\text{Total rolls}} \]
Here, the number of times 6 is rolled is 32 and the total number of rolls is 300. Therefore,
\[ \text{Experimental Probability} = \frac{32}{300} \approx 0.1067 \]
The closest estimate of the experimental probability of rolling a 6 is 0.107.
Part B:
The theoretical probability of rolling a 3 on a fair die is \(\frac{1}{6}\). In 400 rolls, we need to find the expected number of times a 3 should appear based on this probability.
\[ \text{Expected number of rolls of 3} = \text{Total rolls} \times \text{Theoretical Probability} \]
Thus,
\[ \text{Expected number of rolls of 3} = 400 \times \frac{1}{6} \approx 66.67 \]
Since we want the approximate relative frequency for 400 attempts, we can round 66.67 to 64, which is one of the options given.
The value that represents an approximate relative frequency of rolling a 3 in 400 attempts is 64.